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scott <sco### [at] scott com> wrote:
> >> Now simply replace "head being tossed" with "this sequence of characters
> >> being the works".
> >
> > You talk as if I had said somewhere that in the infinite case the
> > probability does *not* equal 1. I don't remember saying such a thing.
> You said:
> > That's, in fact, the exact same thing as saying "never".
> Never is a probability of exactly 0, yet you've just agreed that the
> probability is actually exactly 1. Make your mind up :-)
Great out of context quote.
The "never" was not referring to "will it appear?". It referred to
"is it *forced* to appear"?
No, at no point is it forced to appear. Thus it's *never* forced to
appear. That's not the same thing as "it will never appear".
--
- Warp
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> The "never" was not referring to "will it appear?". It referred to
> "is it *forced* to appear"?
If the probability is exactly 1, which you agree it is, then of course it is
forced to appear at some point in the sequence. If it wasn't then the
probability would be less than 1.
Or are you going to argue now about the meaning of "forced"? ;-)
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scott <sco### [at] scottcom> wrote:
> > The "never" was not referring to "will it appear?". It referred to
> > "is it *forced* to appear"?
> If the probability is exactly 1, which you agree it is, then of course it is
> forced to appear at some point in the sequence. If it wasn't then the
> probability would be less than 1.
And if the probability of getting 0.5 is zero, then of course it means
that it will never be chosen.
Explain to me the exact mechanics which force the works to appear.
--
- Warp
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>> If the probability is exactly 1, which you agree it is, then of course it
>> is
>> forced to appear at some point in the sequence. If it wasn't then the
>> probability would be less than 1.
>
> And if the probability of getting 0.5 is zero, then of course it means
> that it will never be chosen.
Of course.
But the probability of 0.5 turning up is not zero, it is 1/infinity.
Sometimes they can be used interchangably, but in this situation they
cannot. You won't find a mathematician that claims 1/infinity universally
is equal to zero under all circumstances in normal number systems.
On the other hand, writing an infinite sum like 1/2+1/4+1/8+.. does
*exactly* equal one, always, never with any doubt, it is universally
accepted in mathematics.
> Explain to me the exact mechanics which force the works to appear.
Calculate the probability, you will find it is equal to one. Exactly one.
That, by definition, means it is guaranteed, or "forced" if you like, to
happen. QED.
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scott <sco### [at] scottcom> wrote:
> > Explain to me the exact mechanics which force the works to appear.
> Calculate the probability, you will find it is equal to one. Exactly one.
> That, by definition, means it is guaranteed, or "forced" if you like, to
> happen. QED.
Thanks for not answering the question.
--
- Warp
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>> Calculate the probability, you will find it is equal to one. Exactly
>> one.
>> That, by definition, means it is guaranteed, or "forced" if you like, to
>> happen. QED.
>
> Thanks for not answering the question.
Well you can read a few posts back to clear up the detail.
Glad to have helped :-)
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scott wrote:
> But the probability of 0.5 turning up is not zero, it is 1/infinity.
> Sometimes they can be used interchangably, but in this situation they
> cannot. You won't find a mathematician that claims 1/infinity
> universally is equal to zero under all circumstances in normal number
> systems.
>
> On the other hand, writing an infinite sum like 1/2+1/4+1/8+.. does
> *exactly* equal one, always, never with any doubt, it is universally
> accepted in mathematics.
Sorry, but no - the explanation doesn't work. If you read my original
long post, you'd see that the two cases are *identical*.
Getting a sequence of all heads forever is identical to picking a point
from 0 to 1. Both have probability 0. There's a 1-1 correspondence
(which I showed earlier) between the two. They're not just similar -
they're the same.
Conversely, saying that a tails _must_ appear in a sequence is just
doing 1 - (1/2)^n, and taking the limit to infinity, giving 1. Which is
the same as saying that the probability that I _won't_ pick 0.5 when I
choose a number between 0 and 1 is 1.
I even forget how the 1/2 + 1/4 + 1/8 sequence enters the picture - was
that the result of some probability calculation?
>> Explain to me the exact mechanics which force the works to appear.
>
> Calculate the probability, you will find it is equal to one. Exactly
> one. That, by definition, means it is guaranteed, or "forced" if you
> like, to happen. QED.
Yes, by *definition*.
Warp asked for mechanics. Invoking mathematics is not invoking any
physical reasons. The mathematicians have merely defined it that way.
Which does not mean it will happen.
--
"The security of the Enterprise is of Paramount importance.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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John VanSickle wrote:
> The Internet has already proven that a multitude of monkeys would not
> duplicate the works of Shakespeare, regardless of the amount of time
> allowed.
For a very narrow definition of "never".
--
"The security of the Enterprise is of Paramount importance.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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Warp wrote:
> So exactly at which point are the works forced to appear, to fulfill
> the probability of 1?
Infinity. That's the point.
The limit does not equal the value at infinity. Unbounded is not the same as
infinite. You're still confusing the two.
--
Darren New, San Diego CA, USA (PST)
There's no CD like OCD, there's no CD I knoooow!
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Warp wrote:
> Do you disagree that a probability of zero does not mean that the event
> will never happen?
A probability of zero does not mean the event won't happen with an infinite
number of trials. Zero times infinity is not zero.
--
Darren New, San Diego CA, USA (PST)
There's no CD like OCD, there's no CD I knoooow!
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